Welcome to Haverford! This test will help us recommend math
courses that seem right for you. We will make two recommendations: where to
start in our "calculus sequence" and an appropriate statistics course
if you decide to take statistics (either in addition to, or instead of, a
calculus course). In late August, our recommendation will be given to your
faculty advisor and (we hope) emailed directly to you.

Our recommendation is only a first step in finding an appropriate
course for you. Your score on this test will not keep you out of any course
you may want to take; it is just one tool to help you find a course that you
are prepared for and will be challenged by. Once you arrive at Haverford,
you will have several opportunities to discuss course choices with the math
department, your advisor, etc.

The test is divided into five sections -- read the instructions for each
section to see if you should fill out that section

Since the goal of the test is to gauge what Haverford math course would
be best for you, don't guess if you have no idea of the correct answer to
some question; just leave it blank. For the same reason, we see no need for
you to study before taking the test. Finally,...

WHEN YOU ARE DONE, FIND ONE OF THE SUBMIT BUTTONS
AND CLICK IT. (Yes, we already said this, but there's nothing worse than spending
an hour-plus on the test and then failing to submit it...)

Section I: Background Questionnaire
(For all students)

1. Do you think you have a solid background in basic high
school math skills (algebra, geometry, trigonometry)?

Yes
No
Maybe

2. How much calculus have you had?
None
Less than a year
A year or more

3. If you have had calculus, do you feel you know it reasonably
well?
Yes
No
Maybe

4. When was the last time you took math? What course?

5. If you took the AB Calculus Advanced Placement (AP) test,
indicate the result:

Did not take
Have not received results yet
5
4
3
2
1

6. If you took the BC Calculus Advanced Placement (AP) test,
indicate the result:

Did not take
Have not received results yet
5
4
3
2
1

7. If you took the Statistics Advanced Placement (AP) test,
indicate the result:

Did not take
Have not received results yet
5
4
3
2
1

8. Do you plan to take 3 or more semesters of math at Haverford?
Yes
No
Maybe

9. Possible majors

Do you expect to major in math?
Yes
No
Maybe

Do you expect to major in physics?
Yes
No
Maybe

Do you expect to major in chemistry?
Yes
No
Maybe

Do you expect to major in biology?
Yes
No
Maybe

Do you expect to major in economics?
Yes
No
Maybe

Do you expect to major in psychology?
Yes
No
Maybe

Do you expect to pursue the pre-medical curriculum?
Yes
No
Maybe

10. Have you taken a calculus or more advanced course at
a college or university?
Yes
No

If yes, please indicate the class and institution:

11. Have you taken the International Baccalaureat Exam?
Yes
No

If yes, please indicate the results:

12. Please add any brief comments that you think might help
us to recommending an appropriate placement in mathematics:

Section II: Pre-calculus questions
(For all students)

1.

2.

3.

4.

4
100
5
20
None of these

5.

6.

1
2
3
4
5

7.

0
1
2
-2
-1

8. What is the slope of the line joining (0,3) to (6,0)?

1/2
-1/2
-2
2
18

9.

None of the above

10. An equation of the line passing through (-4,0) and (0,-2)
is

None of the above

11.

None of the above

Section III: Derivative and integral
questions (For students who have taken some calculus; if you have not taken
any calculus, click Submit using the button above)

12.

None of the above

13.

None of the above

14.

None of the above

15.

0
1
None of the these

16.

None of the above

17.

None of the above

18.

19.

The balloon reaches its maximum height at t=a

The balloon is dropping fastest at t=b

At t=c, the balloon is below its starting height (i.e., when t=0)

At t=d, the balloon is above its starting height (i.e., when t=0)

None of these statements is true

20.

1/2
1/3
1/4
1
1/6

21.

None of the above

22.

23.

0
1/8
1/4
-1/4
None of these

24.

25.

None of these

26.

Section IV below is just for students who have seen
infinite series in some depth, e.g., in a Calculus BC course.

Section V below
is just for students who have seen enough statistics that they might place
past our introductory statistics course.

If you are in neither of these categories,
then stop now and submit the test using the button below

Section IV: Infinite Series questions
(For students who have seen this material, e.g., in a Calculus BC course;
if you have not seen this material, please scroll down to Section V)

27.

converges to 3/2
converges to 2
converges to 0
converges to 5/3
does not converge

28.

converges to 3/2
converges to 2
converges to 0
converges to e
does not converge

29.

converges to a value less than 0.1

converges to a value between 0.1 and 1

converges to a value between 1 and 2

converges to a value greater than 2

does not converge

30.

31.

1
sin(1)
cos(1)
e
does not converge when x=1

32.

Section V: Statistics (Fill out
this section only if you have taken enough statistics that you think you
might place past our introductory statistics course, e.g., you took and
did well in an AP-level Statistics course).

Within Section V, you may use a calculator.
You should also use a "standard normal table", either your own or the one
that can be downloaded by clicking this link: Standard
Normal Table

33. A description of different houses on the market includes the following
three variables. Which of the variables is quantitative?

The square footage of the house
The monthly gas bill
The monthly electric bill
All of the above

Setup and Figure for Question 34 (five subquestions): In a statistics class with 136 students, the professor records how much money each student has in their possession
during the first class of the semester. The histogram shown below represents the data collected:

34A. What (approximately) is the percentage of students with under $10 in their possession?

35%
40%
45%
50%

34B. Which of the following description(s) is/are correct regarding the shape of the histogram?

Skewed right
Skewed left
Symmetric
All of the above
None of the above

34C. True or False? The histogram indicates the presence of an outlier.

True
False

34D. What is the number of students with $30 or more in their possession?

Less than 5
About 10
About 30
More than 100

34E. From the histogram, which of the following is true?

The mean is larger than the median

The mean is smaller than the median

The mean and median are equal

It is impossible to compare the mean and median given the information available

35. Many residents of suburban neighborhoods own more than one car but consider one of their
cars to be the main family vehicle. The age of these family vehicles can be modeled by a normal
distribution with mean 2 years and standard deviation 6 months. What percentage of family vehicles
is between 1 and 3 years old?

About 68%
About 95%
About 99.7%
Cannot be determined based on the information given

Setup for Question 36 (four subquestions): Central Middle School has
calculated a 95% confidence interval for the mean height
of 11-year-old boys at their school and found it to be 56
2 inches.

36A. True or False: There is a 95% probability that is between
54 and 58.

True
False

36B. True or False: There is a 95% probability that the true mean is 56, and there is a 95% chance that the
true margin of error is 2.

True
False

36C. True or False: If we took many additional random samples of the same size and from each computed a 95%
confidence interval for , approximately 95% of
these intervals would contain .

True
False

36D. True or False: If we took many additional random samples of the same size and from each computed a 95%
confidence interval for , approximately 95% of
the time would fall between 54 and 58.

True
False

37. To assess the accuracy of a laboratory scale, a standard weight that
is known to weigh exactly 1 gram is repeatedly weighed a total of n times
and the mean is computed. Suppose the scale readings are normally distributed
with unknown mean
and standard deviation
= 0.01 g. How large should n be so that a 95% confidence interval for
has a margin of error no larger than
0.0001 g?

n=100
n=196
n=10000
n=38416

38. The scores on the Wechsler Intelligence Scale for Children (WISC) are thought to be normally
distributed with standard deviation = 10.
A simple random sample of 25 children is taken, and each is given the WISC. The mean of the 25 scores is
= 104.32. Based on these data,
what is a 95% confidence interval for ?

104.32 0.78
104.32 3.29
104.32 3.92
104.32 19.60

39. In tests of significance about an unknown parameter, what does the test statistic
represent?

The value of the unknown parameter under the null hypothesis

The value of the unknown parameter under the alternative hypothesis

A measure of compatibility between the null and alternative hypotheses

A measure of compatibility between the null hypothesis and the data

40. The square footage of the several thousand apartments in a new development
is advertised to be 1250 square feet, on average. A tenant group thinks that the
apartments are smaller than advertised. They hire an engineer to measure a sample
of apartments to test their suspicions. Let
represent the true average area (in square feet) of these apartments. What are the
appropriate null and alternative hypotheses?

H0: = 1250 vs.
Ha: < 1250

H0: = 1250 vs.
Ha: 1250

H0: = 1250 vs.
Ha: > 1250

41. A college student is doing some research on the cost of one-bedroom apartments
in town. He has randomly selected 25 apartments for which the price was published.
The average price for these apartments is $652.
He will assume that price follows roughly a normal distribution. Based on prices from previous years,
a real estate agent gives him the information that
is approximately $55. A 95% confidence interval for
the true average price
is found to be 652 21.56 = ($630.44,$673.56).
Determine which of the following statements is true.

A test of the hypotheses H0: = 650 vs.
Ha: 650 would reject the null at the 0.05 level.

A test of the hypotheses H0: = 650 vs.
Ha: > 650
would reject the null at the 0.05 level.

A test of the hypotheses H0: = 675 vs.
Ha: 675 would reject the null at the 0.05 level.

All of the above

42. A test of significance for a null hypothesis has been conducted and the p-value
determined. Which of the following statements about a p-value is true?

The p-value is the probability that the null hypothesis is false.

The p-value is the probability that the alternative hypothesis is true.

The p-value is the probability that the null hypothesis is rejected even if that hypothesis is actually true.

The p-value tells us the strength of the evidence against the null hypothesis. The larger the p-value,
the stronger the evidence against the null hypothesis.

More than one of these statements is true.

None of these statements is true.

Setup for Question 43 (four subquestions): A small company consists of 25 employees. As a service
to the employees, the company arranges for each of the employees to have a complete physical exam for free.
Among other things, the weight of each employee is measured. The mean weight is found to be 165 pounds.
The standard deviation of the weight measurements is 20 pounds. It is believed that a mean weight of 160 pounds
would be expected for this group. To see if there is evidence that the mean weight of the population of all
employees of the company is significantly larger than 160, the hypotheses
H0: = 160 vs.
Ha: > 160 are tested. You obtain
a p-value of about 0.106.

43A. True or False: At the 5% significance level, you have proved that H0 is true.

True
False

43B. True or False: You have failed to obtain any evidence for Ha

True
False

43C. True or False: At the 5% significance level, you have proved that H0 is true
and a larger sample size will be needed to do so.

True
False

43D. True or False: The difference between the observed 165 pounds
and the believed 160 pounds is very significant.

True
False

44. True or False: The power of a hypothesis test will increase when we increase the significance level
.

True
False

45. True or False: The power of a hypothesis test will increase when we increase the sample size.

True
False

46. True or False: The power of a hypothesis test will increase when we consider an alternative value
that is farther from the null value (the parameter of interest under the null hypothesis).

True
False

47. True or False: The power of a hypothesis test will increase when we increase the standard deviation.

True
False

Setup for Question 48 (three subquestions): A simple random sample of 120 vet clinics in the Midwest
reveals that 32 of them treat large animals (cows, horses, etc.). Let p be the population proportion of vet clinics
that treat large animals, and the
sample proportion of vet clinics that treat large animals.

48A. Which is closest to the value of the standard error
of ?

0.02
0.03
0.04
0.05

48B. What is a 90% confidence interval for p?

(0.163,0.371)
(0.188,0.346)
(0.200,0.333)
(0.667,0.800)

48C. If a 95% confidence interval were calculated instead, what would happen to
the width of the confidence interval?

It would be narrower
It would stay the same
It would be wider
This can not be determined from the information given

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